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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Turbulent Mixing Simulation via a Quantum Algorithm

Probability density function (PDF) methods have been very useful in describing many physical aspects of turbulent mixing. In applications of these methods, modeled PDF transport equations are commonly simulated via classical Monte Carlo techniques, which provide estimates of moments of the PDF at arbitrary accuracy. In this paper, recently developed techniques in quantum computing and quantum enhanced measurements (quantum metrology) are used to construct a quantum algorithm that accelerates the computation of such estimates. This quantum algorithm provides a quadratic speedup over classical Monte Carlo methods in terms of the number of repetitions needed to achieve the desired precision. This paper illustrates the power of this algorithm by considering a binary scalar mixing process modeled by means of the coalescence/dispersion (C/D) closure. The equation is first simulated using classical Monte Carlo methods, where error estimates for the computation of central moments are provided. Then the quantum algorithm for this problem is simulated by sampling from the same probability distribution as that of the output of a quantum computer, and it is shown that significantly fewer resources are required to achieve the same precision. Finally, the results demonstrate potential applications of future quantum computers for simulation of turbulent mixing, and large classes of related problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

FIRED (Fire Events Delineation): An Open, Flexible Algorithm and Database of US Fire Events Derived from the MODIS Burned Area Product (2001–2019)

Harnessing the fire data revolution, i.e., the abundance of information from satellites, government records, social media, and human health sources, now requires complex and challenging data integration approaches. Defining fire events is key to that effort. In order to understand the spatial and temporal characteristics of fire, or the classic fire regime concept, we need to critically define fire events from remote sensing data. Events, fundamentally a geographic concept with delineated spatial and temporal boundaries around a specific phenomenon that is homogenous in some property, are key to understanding fire regimes and more importantly how they are changing. Here, we describe Fire Events Delineation (FIRED), an event-delineation algorithm, that has been used to derive fire events (N = 51,871) from the MODIS MCD64 burned area product for the coterminous US (CONUS) from January 2001 to May 2019. The optimized spatial and temporal parameters to cluster burned area pixels into events were an 11-day window and a 5-pixel (2315 m) distance, when optimized against 13,741 wildfire perimeters in the CONUS from the Monitoring Trends in Burn Severity record. The linear relationship between the size of individual FIRED and Monitoring Trends in Burn Severity (MTBS) events for the CONUS was strong (R2 = 0.92 for all events). Importantly, this algorithm is open-source and flexible, allowing the end user to modify the spatio-temporal threshold or even the underlying algorithm approach as they see fit. We expect the optimized criteria to vary across regions, based on regional distributions of fire event size and rate of spread. We describe the derived metrics provided in a new national database and how they can be used to better understand US fire regimes. The open, flexible FIRED algorithm could be utilized to derive events in any satellite product. We hope that this open science effort will help catalyze a community-driven, data-integration effort (termed OneFire) to build a more complete picture of fire.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Solar Flare Prediction Model with Three Machine-learning Algorithms using Ultraviolet Brightening and Vector Magnetograms

We developed a flare prediction model using machine learning, which is optimized to predict the maximum class of flares occurring in the following 24 hr. Machine learning is used to devise algorithms that can learn from and make decisions on a huge amount of data. We used solar observation data during the period 2010–2015, such as vector magnetograms, ultraviolet (UV) emission, and soft X-ray emission taken by the Solar Dynamics Observatory and the Geostationary Operational Environmental Satellite . We detected active regions (ARs) from the full-disk magnetogram, from which ∼60 features were extracted with their time differentials, including magnetic neutral lines, the current helicity, the UV brightening, and the flare history. After standardizing the feature database, we fully shuffled and randomly separated it into two for training and testing. To investigate which algorithm is best for flare prediction, we compared three machine-learning algorithms: the support vector machine, k-nearest neighbors (k-NN), and extremely randomized trees. The prediction score, the true skill statistic, was higher than 0.9 with a fully shuffled data set, which is higher than that for human forecasts. It was found that k-NN has the highest performance among the three algorithms. The ranking of the feature importance showed that previous flare activity is most effective, followed by the length of magnetic neutral lines, the unsigned magnetic flux, the area of UV brightening, and the time differentials of features over 24 hr, all of which are strongly correlated with the flux emergence dynamics in an AR.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Application of Fireworks Algorithm in Gamma-Ray Spectrum Fitting for Radioisotope Identification

We present that identification of radioisotopic signature patterns in gamma-ray spectra is of paramount importance in various applications of gamma spectroscopy. Therefore, there are several active research efforts to develop accurate and precise methods to perform automated spectroscopic analysis and subsequently recognize gamma-ray signatures. In this work, the authors present a new method for radioisotope identification in gamma-ray spectra obtained with a low resolution radiation detector. The method fits the obtained spectrum with a linear combina-tion of known template signature patterns. Coefficients of the linear combination are evaluated by computing the solution of a single objective optimization problem, whose objective is the Theil-1 inequality coefficient. Optimization of the problem is performed by the Fireworks Algorithm, which identifies a set of coefficients that minimize the Theil-1 value. The computed coefficients are statistically tested for being significantly different than zero or not, and if at least one is found to be zero then the Fireworks Algorithm is used to reiterate fitting using the non-zero templates. Fitting iterations are continued up to the point that no linear coefficients are found to be zero. The output of the method is a list that contains the radioisotopes that have been identified in the measured spectrum. The method is tested on a set of both simulated and real experimental gamma-ray spectra comprised of a variety of isotopes, and compared to a multiple linear regression fitting, and genetic algorithm Theil-1 based fitting. Finally, results demonstrate the potentiality of the Fireworks Algorithm based method, expressed as higher accuracy and similar precision over the other two tested methodologies for radioisotope signature pattern identification in the framework of gamma-ray spectrum fitting.

Theil Coefficient↗
DOE OSTI2016

DEVELOPMENT AND TESTING OF FAULT-DIAGNOSIS ALGORITHMS FOR REACTOR PLANT SYSTEMS

Argonne National Laboratory is further developing fault diagnosis algorithms for use by the operator of a nuclear plant to aid in improved monitoring of overall plant condition and performance. The objective is better management of plant upsets through more timely, informed decisions on control actions with the ultimate goal of improved plant safety, production, and cost management. Integration of these algorithms with visual aids for operators is taking place through a collaboration under the concept of an operator advisory system. This is a software entity whose purpose is to manage and distill the enormous amount of information an operator must process to understand the plant state, particularly in off-normal situations, and how the state trajectory will unfold in time. The fault diagnosis algorithms were exhaustively tested using computer simulations of twenty different faults introduced into the chemical and volume control system (CVCS) of a pressurized water reactor (PWR). The algorithms are unique in that each new application to a facility requires providing only the piping and instrumentation diagram (PID) and no other plant-specific information; a subject-matter expert is not needed to install and maintain each instance of an application. The testing approach followed accepted procedures for verifying and validating software. It was shown that the code satisfies its functional requirement which is to accept sensor information, identify process variable trends based on this sensor information, and then to return an accurate diagnosis based on chains of rules related to these trends. The validation and verification exercise made use of GPASS, a one-dimensional systems code, for simulating CVCS operation. Plant components were failed and the code generated the resulting plant response. Parametric studies with respect to the severity of the fault, the richness of the plant sensor set, and the accuracy of sensors were performed as part of the validation exercise. The background and overview of the software will be presented to give an overview of the approach. Following, the verification and validation effort using the GPASS code for simulation of plant transients including a sensitivity study on important parameters will be presented

Fault Diagnosis Algorithm↗
DOE OSTI2023

Optimization Algorithm for Criticality Experiment Design Using Whisper

Many criticality experiments performed to aid in nuclear data evaluation are designed to maximize the sensitivity of the system’s effective neutron multiplication factor to a certain nuclide reaction pair over an energy region of interest. This is typically done by evaluating possible designs in a transport code such as MCNP and selecting the one with the highest desired sensitivity. A designer has many tools to try to maximize this sensitivity such as different moderators, reflectors, fuels, and geometries. This balancing act of identifying a critical and maximally sensitive system become very computationally expensive as more variables are added and higher precisions are desired. In order to identify these optimal configurations more efficiently a Particle Swarm Optimization (PSO) algorithm coupled with MCNP has been developed by Los Alamos National Laboratory (LANL). This algorithm has been used to design two upcoming criticality experiments that will be performed at the National Criticality Experiments Research Center (NCERC), located at the Nevada National Security Site, and operated by LANL, the only general-purpose critical experiments laboratory in the United States. PSO uses a population (swarm) of candidate solutions (particles) on a search space of dimensions such as moderator and reflector thicknesses or enrichments and concentrations. These particles move around the search space from generation to generation according to simple rules. Eventually, the swarm converges on the configuration that is both critical and maximally sensitive to a piece of nuclear data. PSO is well suited for criticality experiments as the algorithm is agnostic to the underlying physics, meaning it is effective on many different experimental setups. This algorithm has been modified to maximize the nuclear data similarity coefficient between an application case and an experiment aimed at replicating the application case using WHISPER, a nuclear criticality safety analysis tool. This allows for the efficient design of critical experiments informed by nuclear data sensitives.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

A Privacy Preserving Distributed Model Identification Algorithm for Power Distribution Systems: Preprint

Distributed control/optimization is a promising approach for network systems due to its advantages over centralized schemes, such as robustness, cost-effectiveness, and improved privacy. However, distributed methods can have drawbacks, such as slower convergence rates due to limited knowledge of the overall network model. Additionally, ensuring privacy in the communication of sensitive information can pose implementation challenges. To address this issue, we propose a distributed model identification algorithm that enables each agent to identify the sub-model that characterizes the relationship between its local control and the overall system outputs. The proposed algorithm maintains the privacy of local agents by only communicating through dummy variables. We demonstrate the efficacy of our algorithm in the context of power distribution systems by applying it to the voltage regulation of a modified IEEE distribution system. The proposed algorithm is well-suited to the needs of power distribution controls and offers an effective solution to the challenges of distributed model identification in network systems.

data-driven modeling↗
DOE OSTI2016

Application of NEM-based Pin-by-Pin HCMFD Algorithm to 3-D Core Analysis

A pin-wise reactor analysis is expected to provide a more accurate solution than the conventional nodal methods. However, a pin-wise approach is still computationally very costly though the computational performances have been enormously improved for decades. To overcome such limitation of a pin-by-pin core analysis, the HCMFD (Hybrid Course-Mesh Finite Difference) algorithm has been recently introduced. By adopting the HCMFD algorithm, a parallel computing can be applied very effectively. In the HCMFD algorithm, an iterative local-global strategy is adopted with a combination of two CMFD acceleration methods for the pin-wise core analysis. The global eigenvalue problem is solved by one-node CMFD, while the local fixed-source problems are solved by two-node CMFD based on the NEM (nodal expansion method). In the HCMFD computational scheme, a parallel computing can effectively be applied since most of the computational efforts are consumed to solve the local problems, and they can be solved in parallel. Previously, only a 2-D HCMFD algorithm was developed and its numerical efficiency was evaluated. In this paper, a 3D HCMFD scheme is introduced and some 3-D problems were analyzed to verify its applicability to 3D pin-wise core analysis. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2014

Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides

The technique that was used to build the EigCG algorithm for sparse symmetric linear systems is extended to the nonsymmetric case using the BiCG algorithm. We show that, similarly to the symmetric case, we can build an algorithm that is capable of computing a few smallest magnitude eigenvalues and their corresponding left and right eigenvectors of a nonsymmetric matrix using only a small window of the BiCG residuals while simultaneously solving a linear system with that matrix. For a system with multiple right-hand sides, we give an algorithm that computes incrementally more eigenvalues while solving the first few systems and then uses the computed eigenvectors to deflate BiCGStab for the remaining systems. Our experiments on various test problems, including Lattice QCD, show the remarkable ability of EigBiCG to compute spectral approximations with accuracy comparable to that of the unrestarted, nonsymmetric Lanczos. Furthermore, our incremental EigBiCG followed by appropriately restarted and deflated BiCGStab provides a competitive method for systems with multiple right-hand sides.

Abdel-Rehim, A M↗
DOE OSTI2016

A rank-exploiting infinite Arnoldi algorithm for nonlinear eigenvalue problems

We consider the nonlinear eigenvalue problem M ( λ ) x = 0, where M ( λ ) is a large parameter-dependent matrix. In several applications, M ( λ ) has a structure where the higher-order terms of its Taylor expansion have a particular low-rank structure. We propose a new Arnoldi-based algorithm that can exploit this structure. More precisely, the proposed algorithm is equivalent to Arnoldi's method applied to an operator whose reciprocal eigenvalues are solutions to the nonlinear eigenvalue problem. The iterates in the algorithm are functions represented in a particular structured vector-valued polynomial basis similar to the construction in the infinite Arnoldi method [Jarlebring, Michiels, and Meerbergen, Numer. Math., 122 (2012), pp. 169–195]. In this paper, the low-rank structure is exploited by applying an additional operator and by using a more compact representation of the functions. This reduces the computational cost associated with orthogonalization, as well as the required memory resources. The structure exploitation also provides a natural way in carrying out implicit restarting and locking without the need to impose structure in every restart. In conclusion, the efficiency and properties of the algorithm are illustrated with two large-scale problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Convergence of the multigrid reduction in time algorithm for the linear elasticity equations

This paper presents some recent advances for parallel-in-time methods applied to linear elasticity. With recent computer architecture changes leading to stagnant clock speeds, but ever increasing numbers of cores, future speedups will be available through increased concurrency. Thus, sequential algorithms, such as time stepping, will suffer a bottleneck. This paper explores multigrid reduction in time (MGRIT) for an important application area, linear elasticity. Previously, efforts at parallel-in-time for elasticity have experienced difficulties, for example, the beating phenomenon. As a result, practical parallel-in-time algorithms for this application area currently do not exist. This paper proposes some solutions made possible by MGRIT (e.g., slow temporal coarsening and FCF-relaxation) and, more importantly, a different formulation of the problem that is more amenable to parallel-in-time methods. Using a recently developed convergence theory for MGRIT and Parareal, we show that the changed formulation of the problem avoids the instability issues and allows the reduction of the error using two temporal grids. We then extend our approach to the multilevel case, where we demonstrate how slow temporal coarsening improves convergence. Finally, the paper ends with supporting numerical results showing a practical algorithm enjoying speedup benefits over the sequential algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Mixed precision s –step Lanczos and conjugate gradient algorithms

Compared to the classical Lanczos algorithm, the s-step Lanczos variant has the potential to improve performance by asymptotically decreasing the synchronization cost per iteration. However, this comes at a price; despite being mathematically equivalent, the s-step variant may behave quite differently in finite precision, potentially exhibiting greater loss of accuracy and slower convergence relative to the classical algorithm. It has previously been shown that the errors in the s-step version follow the same structure as the errors in the classical algorithm, but are amplified by a factor depending on the square of the condition number of the O(s)-dimensional Krylov bases computed in each outer loop. As the condition number of these s-step bases grows (in some cases very quickly) with s, this limits the s values that can be chosen and thus can limit the attainable performance. In this work, we show that if a select few computations in s-step Lanczos are performed in double the working precision, the error terms then depend only linearly on the conditioning of the s-step bases. This has the potential for drastically improving the numerical behavior of the algorithm with little impact on per-iteration performance. Our numerical experiments demonstrate the improved numerical behavior possible with the mixed precision approach, and also show that this improved behavior extends to mixed precision s-step CG. Here, we present preliminary performance results on NVIDIA V100 GPUs that show that the overhead of extra precision is minimal if one uses precisions implemented in hardware.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number

Studying the propagation of uncertainties in a nonlinear dynamical system usually involves generating a set of samples in the stochastic parameter space and then repeated simulations with different sampled parameters. The main difficulty faced in the process is the excessive computational cost. In this paper, we present an efficient, partitioned ensemble algorithm to determine multiple realizations of a reduced Magnetohydrodynamics (MHD) system, which models MHD flows at low magnetic Reynolds number. The algorithm decouples the fully coupled problem into two smaller subphysics problems, which reduces the size of the linear systems that to be solved and allows the use of optimized codes for each subphysics problem. Moreover, the resulting coefficient matrices are the same for all realizations at each time step, which allows faster computation of all realizations and significant savings in computational cost. We prove this algorithm is first order accurate and long time stable under a time step condition. Numerical examples are provided to verify the theoretical results and demonstrate the efficiency of the algorithm.

Jiang, Nan↗
DOE OSTI2025

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗
DOE OSTI2015

Accelerating k-NN Algorithm with Hybrid MPI and OpenSHMEM

Machine Learning algorithms are benefiting from the continuous improvement of programming models, including MPI, MapReduce and PGAS. k-Nearest Neighbors (k-NN) algorithm is a widely used machine learning algorithm, applied to supervised learning tasks such as classification. Several parallel implementations of k-NN have been proposed in the literature and practice. However, on high-performance computing systems with high-speed interconnects, it is important to further accelerate existing designs of the k-NN algorithm through taking advantage of scalable programming models. To improve the performance of k-NN on large-scale environment with InfiniBand network, this paper proposes several alternative hybrid MPI+OpenSHMEM designs and performs a systemic evaluation and analysis on typical workloads. The hybrid designs leverage the one-sided memory access to better overlap communication with computation than the existing pure MPI design, and propose better schemes for efficient buffer management. The implementation based on k-NN program from MaTEx with MVAPICH2-X (Unified MPI+PGAS Communication Runtime over InfiniBand) shows up to 9.0% time reduction for training KDD Cup 2010 workload over 512 cores, and 27.6% time reduction for small workload with balanced communication and computation. Experiments of running with varied number of cores show that our design can maintain good scalability.

Lin, Jian↗
DOE OSTI2026

A Fast Algorithm for Computing Zigzag Representatives

Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with m insertions and deletions can be computed $O(m^ω)$ in time, where $ω < 2.373$ is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^ω)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^3 n)$ time algorithm for this problem, where $n ≤ m$ is the size of the largest complex in the filtration.

Persistent homology↗
DOE OSTI2020

High precision control and deep learning-based corn stand counting algorithms for agricultural robot

This paper presents high precision control and deep learning-based corn stand counting algorithms for a low-cost, ultra-compact 3D printed and autonomous field robot for agricultural operations. Currently, plant traits, such as emergence rate, biomass, vigor, and stand counting, are measured manually. This is highly labor-intensive and prone to errors. The robot, termed TerraSentia, is designed to automate the measurement of plant traits for efficient phenotyping as an alternative to manual measurements. In this paper, we formulate a Nonlinear Moving Horizon Estimator that identifies key terrain parameters using onboard robot sensors and a learning-based Nonlinear Model Predictive Control that ensures high precision path tracking in the presence of unknown wheel-terrain interaction. Moreover, we develop a machine vision algorithm designed to enable an ultra-compact ground robot to count corn stands by driving through the fields autonomously. The algorithm leverages a deep network to detect corn plants in images, and a visual tracking model to re-identify detected objects at different time steps. We collected data from 53 corn plots in various fields for corn plants around 14 days after emergence (stage V3 - V4). The robot predictions have agreed well with the ground truth with C robot =1.02×C human -0.86 and a correlation coefficient R=0.96. The mean relative error given by the algorithm is -3.78%, and the standard deviation is 6.76%. These results indicate a first and significant step towards autonomous robot-based real-time phenotyping using low-cost, ultra-compact ground robots for corn and potentially other crops.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys: A DIRECT-inspired optimization algorithm for experimentally accessible computational material design

Computational materials design has suffered from a lack of algorithms formulated in terms of experimentally accessible variables. Here we formulate the problem of (ternary) alloy optimization at the level of choice of atoms and their composition that is normal for synthesists. Mathematically, this is a mixed integer problem where a candidate solution consists of a choice of three elements, and how much of each of them to use. This space has the natural structure of a set of equilateral triangles. We solve this problem by introducing a novel version of the DIRECT algorithm that (1) operates on equilateral triangles instead of rectangles and (2) works across multiple triangles. We demonstrate on a test case that the algorithm is both robust and efficient. Lastly, we offer an explanation of the efficacy of DIRECT -- specifically, its balance of global and local search -- by showing that 'potentially optimal rectangles' of the original algorithm are akin to the Pareto front of the 'multi-component optimization' of global and local search.

97 MATHEMATICS AND COMPUTING↗